Prayer, simply put, is communication with God. St John Damascene once said, “Prayer is the raising of one's mind and heart to God or the requesting of good things from God”. In other words, it is an action where an individual reaches out to God, for a litany of reasons. The Catechism of the Catholic Church (CCC) identifies 3 methods of prayer - Vocal, Meditative and Contemplative prayer.
Vocal Prayer is a method of prayer where one uses their voice in order to establish their communication. This is done, quite literally, by saying words out loud to offer prayer and testimony to God. This is typically done in groups, one instance would be a family saying grace before dinner.
Meditative prayer involves an engaged form of mental activity. This is where one reflects on a specific action, passage, or person in an effort to grow closer to God. For example, if someone reads the passage of the prodigal son in the Gospel, they may take some time to reflect on its meaning, or sit in silence and think about the story, its messages, parallels in their life, etc. This is meditative prayer. They are communicating with God, not by speaking, but by meditating on some aspect of Faith.
Contemplative prayer may seem similar to Meditative prayer, but they are different. The Catechism states:
Contemplative prayer is the simple expression of the mystery of prayer. It is a gaze of faith fixed on Jesus, an attentiveness to the Word of God, a silent love. It achieves real union with the prayer of Christ to the extent that it makes us share in his mystery.
The main distinction of contemplative prayer is it extends beyond mediation. In meditation, a person is making an engaged effort to focus on an aspect of Faith. In contemplation, they are no longer making an effort, but they are still immersed, through the Holy Spirit, in God’s goodness. In the words of St. Alphonsus, “In meditation, God is sought after by a discursive effort; in contemplation there is no effort of this kind, as God has been found and is gazed at.” Below is a video with more information on Catholic Prayer: